CAREER: High-dimensional inference and applications to modern biology

近年来，高维统计推断的一个新兴领域取得了惊人的进步，为越来越多的统计和机器学习方法提供了新的理论工具来表征准确的分布行为。这些进展有望改进统计程序，对现代生物学许多领域的不确定性进行更精确的量化。这项研究将扩大这些高维推理方法的范围，目前这些方法仍然局限于更程式化的统计模型，以解决具有复杂潜在结构的更广泛的科学问题。这项研究还将使PI能够继续他在康涅狄格州公立学校的K-12级别的教育外展活动，以及他在耶鲁大学的入门课程教学中的实验，通过集中讨论统计概念和想法来激发现实生活中的例子。在理论方面，本研究将提高我们对非I.I.D.平均场现象的理解。背景，包括具有统计相关耦合的无序系统和自旋玻璃模型，以及具有相关设计的回归模型的变分贝叶斯近似。这一研究也将进一步加深我们对统计背景下随机矩阵模型的渐近自由性现象的理解。在应用方面，这项研究将提高我们对基于似然推理的低温电子微结构确定的理解，并探索更健壮和高效的重建算法的可能性。这项研究还将开发新的贝叶斯和经验贝叶斯程序，用于精细绘制遗传因果变量图和基因序列数据降维。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

In recent years, a burgeoning field of high-dimensional statistical inference has witnessed astounding advances, providing new theoretical tools to characterize exact distributional behavior for an increasingly large class of statistical and machine-learning methods. These advances hold the promise of improved statistical procedures with more precise quantifications of uncertainty across many fields of modern biology. This research will extend the scope of these high-dimensional inferential methods, which currently remain restricted to more stylized statistical models, to address a broader range of scientific problems having complex latent structure. The research will also enable the PI to continue his educational outreach activities in the K-12 levels in Connecticut public schools, as well as his experimentation in the teaching of introductory courses at Yale University by focusing the discussion of statistical concepts and ideas on motivating real-life examples.On the theoretical front, this research will improve our understanding of mean-field phenomena in non-i.i.d. contexts, including disordered systems and spin glass models with statistically dependent couplings, as well as variational Bayesian approximations to regression models with correlated designs. This research will also further our understanding of asymptotic freeness phenomena for random matrix models arising in statistical settings. On the applications front, this research will improve our understanding of likelihood-based inference for molecular structure determination in cryo-electron microscropy, and investigate possibilities for more robust and efficient reconstruction algorithms. This research will also develop new Bayes and empirical Bayes procedures for fine-mapping of genetic causal variants and for dimensionality reduction of genetic sequence data.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.